Young's double slit experiment is carried out by using green, red and blue light, one color at a time. The fringe width recorded are `b_(G)`,`b_(R)` and `b_(B)` respectively. Then,

Options

A. `beta_(G) gt beta_(B) gt beta_(R)`
B. `beta_(B) gt beta_(G) gt beta_(R)`
C. `beta_(R) gt beta_(B) gt beta_(G)`
D. `beta_(R) gt b\eta_(G) gt beta_(B)`

Explanation

To solve the problem regarding the fringe widths in Young's double slit experiment using different colors of light (green, red, and blue), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Fringe Width Formula**:
The fringe width (β) in Young's double slit experiment is given by the formula:
\[ \beta = \frac{\lambda D}{d} \]
where:
- \( \beta \) = fringe width
- \( \lambda \) = wavelength of the light used
- \( D \) = distance from the slits to the screen
- \( d \) = distance between the slits

2. **Identifying Constants**:
In this experiment, \( D \) and \( d \) are constants for a given setup. Therefore, the fringe width is directly proportional to the wavelength (\( \lambda \)):
\[ \beta \propto \lambda \]

3. **Comparing Wavelengths**:
The wavelengths of the colors in the visible spectrum are approximately:
- Red light (\( \lambda_R \)) has the longest wavelength.
- Green light (\( \lambda_G \)) has a medium wavelength.
- Blue light (\( \lambda_B \)) has the shortest wavelength.

Thus, we can establish the order of wavelengths:
\[ \lambda_R > \lambda_G > \lambda_B \]

4. **Relating Fringe Widths**:
Since fringe width is directly proportional to wavelength, we can write:
\[ b_R > b_G > b_B \]
This means:
- The fringe width for red light (\( b_R \)) is the largest.
- The fringe width for green light (\( b_G \)) is in the middle.
- The fringe width for blue light (\( b_B \)) is the smallest.

5. **Final Relationship**:
Therefore, the relationship between the fringe widths is:
\[ b_R > b_G > b_B \]